It's a good idea. But I have some concerns:
1.) Do you think Luna is that vulnerable from a cockatrice? I mean, she and Celestia are almost equal as alicorns and divine beings.
2.) Why would it take place when Discord is on the loose? Isn't the fact that Discord on the loose is more important than a missing Luna?
3.) Can you think of other ways to break Luna's petrification aside from Fluttershy's Stare? In my opinion, it's already been used.
1. Normally no she wouldn't be. I mean she'd have to be ambushed by an army normally doing some kind of combo on her making her open her eyes in time for their stare to work. But if someone else attacks her & uses one like a weapon while forcing her eyes open that would work. An ambush is perfect for that. It's unexpected, Luna can't guard against it in time, & can be beaten easily if turned to stone.
2. Well Discord isn't causing as much problems as he did in Return of Harmony. Rather he's trying his hand at being a peaceful spirit causing chaos here & there with responsibility. I.E. he's learning from his past 2 defeats & figured that if he wants to cause chaos & not be turned back to stone he better stay in tune with the Balance & not go crazy with the chaos & Make it fun for everypony instead of mean like he did when he discorded the Mane 6. Plus if Luna's missing that's a serious problem. EVen Discord would agree with that. Also if an Alicorn Princess is turned to stone one would agree that Discord could wait til everything else is fixed. Plus Discord would believe that no one deserves that fate of being turned to stone. I mean who would? It's a little extreme & worse than Death.
3. Hmm...well we could bring in the concept of Gold Needles which are suppose to cure The Stone/Petrified status. Unless someone knows of a stone freeing spell.
Also I just thought of a little more for the plot. For the plot to be more interesting we can make it when the investigation happens be 4 or 5 days later after Luna's disappearance & petrification to have Celestia be very worried thus prompting the Guards & all to be on high alert for her.